The next building after the Singer Building to hold the record for the world's highest was the Metropolitan Life Insurance Tower, located in Midtown Manhattan at Madison Square. It held the title from 1909 to 1913, around the time when the above photo was taken.
The photo above, taken between 1909 and 1920, shows the tower at night, with Madison Square in the foreground.
Although the tower was built in 1909, the rest of the building was older. The above photo, taken around 1900, shows the Metropolitan Life Insurance Building (built in 1893) prior to the construction of the 50-story tower. The tower was built at the site of the church on the left-hand side of the picture, Madison Square Presbyterian Church.
The company later built another building just to the north in order to add office space for the growing company, and in the 1950s the original 1893 building (but not the tower) was replaced by the current building.
This view of the Metropolitan Life Insurance Tower, taken from the Empire State Building in January 2011, shows the 1909 tower just to the right of center. Notice that just beyond the tower, at the base, is the building that replaced the original 1893 office building in the 1950s. On the other side of the tower, in the center of the photo, is the North Building, which was completed in 1950. These buildings served as the headquarters of Met Life until 2005. As of now, there are plans to convert the tower into a hotel.